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1 ESSAYS ON THE ECONOMICS OF MARRIAGE DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Alita Nandi, M.A. * * * * * The Ohio State University 2007 Dissertation Committee: Professor Audrey Light, Advisor Professor Stephen Cosslett Professor Randall Olsen Approved by Advisor Economics Graduate Program

2 Copyright by Alita Nandi 2007

3 ABSTRACT Recent U.S. policies that promote marriage have prompted researchers to reexamine the reasons for the fact that black marriage rates are more than 20 percentage points lower than white marriage rates. In the first essay, The Role of Education in the Marital Decisions of Blacks and Whites I ask how much of the black-white marriage gap would be eliminated if racial differences in schooling attainment were reduced. I use data from the 1979 National Longitudinal Survey of Youth to simultaneously estimate schooling and marriage models. I find that increasing the schooling of black men by one year increases the predicted probability of marriage (by age 35) by more than 5%. The estimated effect is much smaller for white men and black women, and it is negative for white women. Using these estimated coefficients, I predict that eliminating black-white differences in schooling (which I simulate by assigning all blacks the mean schooling of their white counterparts) would decrease the gap in marriage probabilities by 17% for men and 4.5% for women. I conclude that public policy designed to increase education can have small but nontrivial effects on the black-white marriage gap. U.S. public policy promotes both marriage and labor market participation as strategies for improving the economic welfare of low-income women and their children. In the second essay, Women s Economic Gains from Employment, Marriage and Cohabitation I ask which of these mechanisms (marriage or employment) leads to greater economic gains especially for those women who are predisposed towards poverty. In light of the dramatic rise in cohabitation rates in recent years, I also include cohabitation as a third mechanism for improving well-being. Using data from the 1979 National Longitudinal Survey of Youth, I estimate a fixed-effects model of household income (adjusted for household composition) to assess the within-person gains associated with changes in employment and marital status; I allow the effects of employment on ii

4 household income to differ for single, cohabiting, and married women. Focusing first on poor women (those who ever received welfare), I predict that the log household income of single, nonemployed women increases by 0.80 if they enter a cohabiting union, 1.04 if they marry, 0.76 if they work part-time (1000 hours/year), and 1.16 if they work full-time (2000 hours/year). The finding that the biggest predicted gain is from entering full-time employment (while remaining single) reflects the fact that the expected earnings of these low-wage women exceeds the share of adjusted earnings that they can be expected to gain by marrying a (typically low-wage) man. When I consider transitions of women who are already employed part-time, I find that their expected gains from cohabitation and marriage are virtually identical (0.48 and 0.47, respectively) and that union formation now has a greater expected benefit than moving to full-time employment, which I predict raises log income by When I focus on nonpoor women, I find that single, part-time employed women are expected to gain 0.64, 0.56 and 0.54, respectively, when they enter a cohabiting union, marry and move to full-time employment; each of these gains is greater than what I predict for their poor counterparts. This is not surprising given the higher earnings potential of these women as well as that of their spouses and partners. iii

5 ACKNOWLEDGMENTS I am deeply indebted to Audrey Light. Without her encouragement and her help in every aspect of my research, this dissertation could not have been written. It has been a privilege to have her as my advisor. I am grateful to Stephen Cosslett and Randall Olsen for their insightful comments and suggestions. I would also like to thank Xiaohong Angerer, Deepankar Basu and Rosella Gardecki for their valuable help and support. I am thankful to the Ohio State University and the Center for Human Resource Research for financial assistance and to the Department of Economics, the Ohio State University and the Center for Human Resource Research for providing me with their research facilities. iv

6 VITA November 4, Born - Indore, India B.S., Economics, University of Calcutta M.A, Economics, Jawaharlal Nehru University, M.A., Economics, Ohio State University Teaching Assistant, Department of Economics, the Ohio State University 2001 Present...Graduate Research Associate, Center for Human Resource Research, the Ohio State University PUBLICATIONS Identifying Race and Ethnicity in the 1979 National Longitudinal Survey of Youth, (with A. Light), Population Research and Policy Review (forthcoming) FIELDS OF STUDY Major Field: Economics v

9 LIST OF TABLES Tables Page 2.1 Sample Selection Criteria Fraction Ever Married (by Age 35) by Educational Attainment, Race and Sex Distribution of Educational Attainment by Race and Sex (Fraction of Race Sex Sample in Different Schooling Categories Means and Standard Deviations of Selected Variables Marginal Effects and Z-statistics, 2 nd Stage Estimates of Ever Married by Age 35 (Based on Joint Estimation of Schooling and Marriage) Coefficients and Z-Statistics, 2 nd Stage Estimates of Ever Married by Age 35 (Based on Joint Estimation of Schooling and Marriage) Coefficients and T-statistics, 2 nd Stage Estimates of HGC by 1 st Marriage or Age 35 (Based on Joint Estimation of Marriage and Schooling) Marginal Effects and Z-statistics, Probit Estimates of Ever Married by Age 35 (Schooling is Treated as Exogenous) Marginal Effects and Z-statistics, 2 nd Stage Estimates of Ever Married by Age 25 (Based on Joint Estimation of Schooling and Marriage) viii

10 2.10 Expected Male Marriage Rates (Computed Using 2 nd Stage Estimates of Ever Married by Age 35, see Table 2.6) Expected Female Marriage Rates (Computed Using 2 nd Stage Estimates of Ever Married by Age 35, see Table 2.6) Blinder-Oaxaca Type decompositions for Black-White Differences in Marriage Rates, Computed Using 2 nd Stage Estimates of Ever Married By Age 35 (Based on Joint Estimation of Marriage and Schooling (See Table 2.6)) Coefficients and T-statistics, 1 st Stage Estimates of HGC by First Marriage or Age 35 (Based on Joint Estimation of Marriage and Schooling) Coefficients and Z-statistics, 1 st Stage Estimates of Ever Married by Age 35 (Based on Joint Estimation of Marriage and Schooling) Distribution of Observations per Woman Comparing Average Household Income of Married and Cohabiting Woman with that of Single Women Summary Statistics Coefficients and Standard Errors Based on First-Difference Estimation of Log Household Income Predicted Change in Log Household Income Based on First-Difference Estimations Predicted Percentage Change in Household Income Based on First-Difference Estimations ix

11 3.7 Coefficients and Standard Errors Based on OLS Estimation of Log Household Income Predicted Change in Log Household Income Based on OLS Estimations Predicted Percentage Change in Household Income Based on OLS Estimations Summary Statistics for Hispanics, Blacks and Never on Welfare sub-samples Coefficients and Standard Errors Based on First-Difference Estimation of Log Household Income for Hispanics, Blacks and Never Received Welfare sub-samples Predicted Change in Log Household Income Based on First-Difference Estimations for Hispanic, Black and Never Received Welfare Sub-samples Predicted Percentage Change in Household Income Based on First-Difference Estimations for Hispanic, Black and Never Received Welfare Sub-samples x

12 CHAPTER 1 INTRODUCTION In recent years marriage has occupied an increasingly prominent place in public debates and discussions. It has been thrust into the public eye through the Personal Responsibility and Work Opportunity Reconciliation Act of 1996 (PRWORA) and later received a boost by President Bush s Healthy Marriage Initiative in 2004 which proposed to spend around $300 million every year for the next five years to promote healthy marriages. As a result some economic and non-economic policies to promote marriage were introduced. 1 This renewed interest in marriage promotion prompted researchers to reexamine the issue of the determinants of marriage (Alm and Whittington 1999, Lichter et al. 2002, Loughran 2002). Estimating economic gains from marriage, especially that of women, is another area of research that has received considerable attention in recent years (Bianchi et al. 1999, Smock et al. 1999, Thomas and Sawhill 2002, Lichter et al and Light 2004). This is because the primary justification for promoting marriage is the belief that marriage can improve the economic welfare of lowincome women and their children and enable them to move out of poverty. In this dissertation I examine some specific issues in these two areas of research determinants of marriage and women s economic gains from marriage. 1 For example, since 1996 West Virginia offers married couples on welfare a cash incentive of $100 per month ( In 1997 Louisiana passed a covenant marriage law and Arizona and Arkansas have followed suit ( Seven states (Arizona, Louisiana, Michigan, New Mexico, Oklahoma, Utah, and Virginia) spend significant TANF funds on activities specifically designed to strengthen marriage and parental relationships (Parke 2004). The federal marriage penalty tax was substantially reduced through the Jobs and Growth Tax Relief Reconciliation Act of

13 It is well established that public policy affects schooling attainment. The crucial question is whether marriage can be positively affected by schooling and thus whether schooling can serve as an implementable marriage promotion policy. For efficient use of public funds it is important to know whether schooling will be equally effective in promoting marriage across different racial groups. This provides the motivation for my first essay, The Role of Education in the Marital Decisions of Blacks and Whites where I estimate the effect of schooling attainment on the marriage probabilities of blacks and whites. Specifically, I ask how much of the black-white difference in marriage rates stems from differences in schooling. Would the black-white gap in marriage rates change if the schooling of blacks were exogenously changed? Finally, if schooling levels of blacks were simulated to be the mean schooling of whites then what would be the predicted difference in black-white marriage rates? It is widely believed that marriage results in economic benefits for women and their children and two studies have corroborated this belief (Smock et al and Light 2004). Smock et al. (1999) find that women suffer economic losses upon divorce and Light (2004) finds that they experience an economic gain if they marry or enter a cohabiting union. These studies, however, do not tell us whether the economic gains from marriage and cohabitation for low-income women, the marriage-promotion policy target group, are different from that of the general population. The PRWORA emphasizes employment and marriage as two mechanisms to move out of poverty. In light of that it is interesting to know how a woman s gains from marriage compare with her gains from changing employment intensity. There are no studies which address this issue. To the best of my knowledge all public policies that are concerned with the welfare of lowincome women and their children ignore cohabitation as an alternative mechanism. Given the dramatic rise of cohabitation in recent years, I agree with existing studies in treating it as a living arrangement alternative to marriage (Thornton et al. 1995, Raley 1996, Light 2004) and include it as a third mechanism for improving a woman s economic wellbeing. In my second essay, Women s Economics Gains from Employment, Marriage and Cohabitation, I attempt to fill in these gaps. Specifically, I ask the following. What are the economic gains that any single poor woman would experience if she were to 2

14 cohabit, marry or change her employment intensity? I find that the difference in household incomes of married or cohabiting women and single women vary by their employment levels (hours worked) which prompts me to ask how these estimated gains vary by a woman s initial hours worked. Finally, I ask how the estimated gains for poor women differ from that of the full-sample. To be able to answer the questions that I have posed in these essays it is necessary to identify the effects of the variables of interest effect of schooling on marriage probabilities and the effect of marital status and hours worked on household income. If there were no unobservable (to the econometrician) factors that were correlated with the variables of interest and the dependent variables in each of these cases then estimating marriage probabilities by Probit and estimating household income by Ordinary Least Squares would have been sufficient to identify the causal effects of the variables of interest on the dependent variables. Existing studies show that this is not a justified assumption (Boulier and Rosenzweig 1984, Sander 1992, Light 2004) and appropriate estimation methods need to be used. In the first essay, I identify the effects of schooling on marriage probabilities by simultaneously estimating a static model of marriage and schooling using a two-stage estimation methods suggested by Lee and Maddala (1976) and Heckman (1978). In the second essay, I compute the first-difference estimator to identify the effect of marital status and hours worked on household income. This identification of causal effects is conditional on the assumption of strict exogeneity of the variables of interest conditional on the individual-specific time-invariant unobserved factor. Using a test suggested by Wooldridge (2002) I find that this exogeneity condition holds. In both these essays I use data from the 1979 National Longitudinal Survey of Youth. 3

15 CHAPTER 2 THE ROLE OF EDUCATION IN MARITAL DECISIONS OF BLACKS AND WHITES 2.1 Introduction Black-white differences in marital behavior in the United States are well documented and extensively studied. The striking patterns are that blacks have lower marriage rates than whites and, on average, marry at a later age than whites (Espenshade 1985, Mare and Winship 1991, DHHS 2002). Schooling attainment patterns mirror these marriage patterns in that blacks have lower average levels of educational attainment than whites (Smith and Welch 1989, Cameron and Heckman 2001). A positive correlation between marriage probabilities and educational attainment, especially for blacks, has also been observed (Lichter et al. 1992, Oppenheimer et al. 1997). In this paper, I ask how much of this black-white difference in marriage rates is due to differences in schooling. Would black-white differences in marriage rates change if the schooling levels of blacks were exogenously changed? If blacks were assumed to have the same average schooling as whites how much of the marriage gap would remain? Public policies to promote marriage such as tax laws, marriage covenant marriage laws and cash incentives to welfare participants to get married have been prevalent for quite some time. One of the few studies to measure the effectiveness of public policies on marriage has looked specifically at the impact of tax laws and found very limited effect (Alm and Whittington 1999). To structure an effective marriage promotion policy it is imperative to identify key determinants of marriage probabilities that can be significantly influenced by public policy. While schooling attainment can be impacted by public policy, it remains to be seen whether it is a key determinant of marriage promotion. Also, 4

16 if the goal of public policy is to promote marriage, it is important to understand why some demographic groups are less likely than others to marry. To analyze the link between schooling and marriage, I simultaneously estimate a static model of marriage and of schooling using a two-stage estimation method suggested by Lee and Maddala (1976) and Heckman (1978). In light of evidence that schooling decisions may be endogenous to marriage decisions (Boulier and Rosenzweig 1984, Sander 1992, Goldin 1995 and Gould 2003), I use this method to identify the effect of schooling on marriage probabilities. I do not control for employment and earnings in order to identify the total effect of schooling, including the effect of employment and earnings that are partly determined by schooling. I use data from the 1979 National Longitudinal Survey of Youth (NLSY79). This survey is particularly suited for my study because it over-samples blacks and collects detailed information about schooling and marital activities and background information such as religious affiliation, parental education and family structure. Moreover, respondents have been followed from 1979 when that were between the ages of 14 and 22. I use data until 2002 (2004 is the last year for which data available), when they were between the ages of 37 and 45. I use the variable ever married by age 35 as a proxy for the variable ever married. I estimate the model separately by race and sex and find that the schooling of all groups except white women has a positive effect on the probabilities of being married by age 35. I compute a Blinder-Oaxaca-type decomposition for the black-white marriage gap (Even and Macpherson (1990, 1991) and Fairlie (1999, 2003)). Using estimates of schooling coefficients for blacks I find that black-white differences in men s (women s) schooling explains 17.5% (4.5%) of the difference in their marriage probabilities. In addition, using these estimated schooling coefficients, I predict that elimination of blackwhite differences in schooling (which I simulate by assigning to all blacks the mean schooling of their white counterparts) would decrease the gap in marriage probabilities by 17.2% for men and 4.5% for women. When I carry out a similar exercise, but instead assign 16 or more years of completed schooling to all black men, the expected black- 5

17 white male marriage gap is only 6%. I conclude that public policy designed to increase education can have small but nontrivial effects on marriage rates as well. 2.2 Background Becker (1973) was one of the first persons to conceptualize marriage as being driven by the utility maximizing behavior of rational economic agents. In Becker s model this utility is derived from tangible and intangible goods produced by the household using as inputs the time of household members and goods purchased in the market with their joint earnings. Becker s static model with perfect information was later modified to accommodate the dynamic nature of marital decisions as well as the cost of searching for a mate (Oppenheimer 1988 and Burdett and Coles 1997). Thus, two persons decide to marry if their expected lifetime utility from this match is greater than that of remaining single and continuing searching. It follows that a person s decision to accept a marriage offer depends not only on the characteristics of that match but also of those of all other participants in the marriage market. Using this framework I would like to explain how schooling and marriage are expected to affect each other and how these effects are likely to differ for men and women and blacks and whites. The presence of economies of scale in household production, public goods and complementarity in consumption would make the joint utility that a couple gets from a given level of joint income to be more than the sum of utility that they would have derived if they were living in separate household with no change in their own earnings. After marriage, spouses may also change their participation in the labor market and household production in such a way that their joint utility increases. If the wage of one spouse is greater than that of the other and the opposite is true for their marginal product of household production then the spouse with the lower labor market wage would specialize in the labor market to increase their overall household utility. It is well established that one method of improving the economic conditions of individuals is to increase schooling (Griliches 1977, Blackburn and Neumark 1993, Butcher and Case 1994, Ashenfelter and Krueger 1994 and Card 1999). A higher 6

18 schooling thus signals a higher future income, more precisely labor market earnings. The higher a person s market wage, the more likely is such a person to meet those with market wages lower than his/her own. In such a scenario, it is more likely that this person would specialize in labor market and his/her spouse in household activities. In other words, a successful match would require this person to be matched with a person with a comparative advantage in household production. Social norms in the U.S. until recently (1960s) dictated that women specialize in household production and men in the labor market (breadwinner-homemaker household structure) and so a man with higher earnings is more likely to marry than a man with lower earnings. Social norms respond slowly to changes in the underlying economic environment. Labor market participation and labor market skills of women have since increased relatively more than men s comparative advantage in household production has. Under these circumstances a woman with higher earnings is less likely to find a man with better household skills than her and so one could expect women s probability of marriage to decline with their labor market earnings. Men with higher labor market earnings are more likely to find women with a comparative advantage in household production and so will have higher marriage probabilities. In a household model where there is consumption of public goods within the household and some goods are produced in the household using time inputs, positive assortative mating will increase as the level of public goods increases (Lam 1988). Also, as household income rises the amount of public goods within a household also goes up and so the degree of positive assortative matching on wages increases. This implies men and women with higher market wages are more likely to be married. Oppenheimer (1988) argues that because women with higher earnings will have higher economic independence and higher bargaining power within the household, they will raise their reservation levels. These women will be more interested in pre-marital matching on lifestyles than on their post marital adaptation to their husband s lifestyles and thus search longer. This would imply that women with higher schooling are less likely to get married early, if at all. In addition to the above factors schooling is likely to increase marriage probabilities of both men and women because colleges and universities act as marriage 7

19 markets with very low search costs (Goldin 1995). Schooling is also a desirable marriageable trait because it may increase the gains to marriage by increasing the labormarket productivity of the spouse. Benham (1974) finds this is true of women. To summarize, the effect of schooling on marriage probabilities is expected to be positive for men but is ambiguous for women. Smith and Welch (1989) conclude that schooling is a major source for closing the black-white wage gap. They also find that the labor market returns to schooling are higher for black men as compared to white men for cohorts entering the labor market in the late 1970s. Also, given the lower average schooling levels among blacks, the availability of potential mates (who would accept a marriage offer) for black men with high schooling would be higher than for white men. These imply that the effect of schooling on marriage probabilities is likely to be higher for black men than for white men. Less is known about the difference in the schooling effects for black and white women. Schooling choice, like marriage decisions, is also driven by utility maximization (Becker 1962, 1993 and Mincer 1974). Individuals choose the amount of schooling that will maximize their net expected lifetime benefits. The costs are mainly tuition costs, other related expenses, foregone earnings and any disutility from learning. The benefits are higher future earnings, utility from knowledge and network externalities. The role of marriage returns in school choice is ambiguous. Those with high returns to marriage who find suitable marriage offers in order to get married would drop out of school and enter the labor market. Others also with high returns from marriage but no suitable marriage offers may acquire higher schooling in order to increase their marriageability. The above discussion directs our attention to the possibility that while schooling may affect marriage probabilities returns to marriage may also affect schooling choice; i.e., schooling is endogenous to marriage probabilities. This poses some problems for estimation of the causal effect of schooling on marriage probabilities. It is important to note that some factors such as ability, perseverance and determination that affect both a person s marriage probabilities and schooling choice but are not observed by the 8

20 econometrician also contribute to this estimation problem. I will discuss these estimation issues in a later section. Most studies that consider the effect of schooling on own marriage probabilities of blacks and whites have ignored the possibility that returns to marriage could affect schooling decisions. Here I briefly summarize the results of some of these studies. Goldscheider and Waite (1986) and Lichter et al. (1992) find that educational attainment is positively correlated with marriage probabilities of women between the ages of approximately years. Goldscheider and Waite (1986) and Oppenheimer et al. (1997) find that schooling is positively correlated with men s marriage probabilities while Lloyd and South (1996) find that the opposite is true. Although Lloyd and South (1996) and Oppenheimer et al. (1997) both used NLSY79, the former followed the sample until the respondents were 18 to 27 years of age while the latter followed them until they were 24 to 33 years old. The inconsistency of these results could be explained by the effect of schooling on marital decisions and vice versa. Thornton et al. (1995) found school enrollment to have a negative impact on marriage probabilities. Hence at younger ages when individuals have to make the choice between schooling and marriage, those with higher returns to marriage choose higher schooling and postpone marriage. Later in life after they have established their careers their higher earnings results in higher marriage probabilities. On the other hand, those with lower returns to marriage choose lower schooling. Some of them get married. Because of their low schooling their probabilities of marriage does not increase later in life (unlike those with higher schooling). It follows that there will be a negative correlation between schooling and marriage for young persons and the opposite for older persons. Boulier and Rosenzweig (1984) addressed the issue of endogeneity of schooling to marriage probabilities when investigating marital behavior of women in the Philippines and found that unobservable variables that drive women to acquire higher schooling also drive them to search for a mate longer. Sander (1992) used a Hausman test to show that schooling may be endogenous to marriage probabilities for white men in the U.S. Gould (2003) found that white men with higher returns from marriage tend to acquire higher schooling and choose higher paying jobs/occupations. Goldin (1995) 9

21 provided a descriptive analysis of marital and schooling behavior of women in the U.S. over the last few decades and found that women born in the 1930s went to college more to tap into the marriage market than to pursue a career with higher future labor market earnings. None of these studies have estimated causal effect of schooling on marriage probabilities of blacks or white women in the U.S. and so my study is perhaps the first attempt to identify the causal effect of schooling on marriage probabilities of blacks and whites and to use these estimated effects to explain the racial difference in marriage rates caused by racial difference in schooling. Some of the key studies that have tried to explain black-white differentials in marriage rates have emphasized the importance of the marriage market rather than just a person s own characteristics. Wilson (1987) introduced the idea of a male marriageable pool index (the ratio of employed men to women) to emphasize that the lack of marriageable men rather than changing social trends or welfare programs was the most important reason for the rise in the incidence of nonmarital pregnancies among black women. Other studies using more sophisticated measures of mate availability have found correlations between marriage rates and mate availability (Lichter et al. 1992, South and Lloyd 1992). Unlike other studies, Wood (1995) identified the causal effect of availability of marriageable men (men with good economic prospects) on marriage rates and found that only about 3% to 4% of the decline in black female marriage rates could be explained by the drop in the number of black men with good economic prospects. 2.3 A Model of Marital Choice The Decision-Making Process The discussion on marital and schooling choices in the last section provides the background for the marriage and schooling equations that I estimate. In this study I am interested in estimating the effect of schooling on a never married person s probability of first marriage (equivalent to lifetime marriage probabilities). Among never married persons I do not distinguish between those who are cohabiting with a partner and those who are not. While both marital and schooling decisions are dynamic in nature, because 10

22 my interest is only in the probability of being ever married, I concentrate on the static choice among never married persons of being ever married and on the schooling they acquire prior to their first marriage. 2 We rarely get observations spanning the entire life of an individual and so we have to choose a certain age to represent ever in ever married; as discussed in section 2.4.2, I use age 35. To identify the effect of schooling on the probability of being ever married, I consider schooling at the time of first marriage or, for those who never marry by age 35, schooling by this age. One problem with using pre-marital schooling in understanding the effect of schooling on marriage probabilities is that sometimes individuals plan to continue schooling after they get married and they do so. In such a case the post-marital schooling should be considered in determining marriage probabilities rather than premarital schooling. However, I cannot distinguish between those who planned to continue school before they got married and those who acquired additional schooling as a consequence of being married, so I ignore post-marital schooling. i The linearized expected net gain from (first) marriage for a never married person can be written as * (1) M = V ( X, S ) + ε for i i which can be linearized to * (2) M i = θ + α X i + βsi + ε i i i i i = 1,2,...N where S i measures pre-marital schooling attained by person i. Other observed factors are represented by X i and unobserved factors are represented byε. The parameters to be i estimated areθ, α and β. I normalize the parameters associated with benefits from not marrying to 0. Thus, (3) M i * 1 if M i > 0 = 0 otherwise 2 In estimating a static model, however, I will not be able to estimate time-varying parameters. 11

23 where M i is the dummy variable indicating whether a never married person i chooses to marry or to remain single. The optimal pre-marital schooling level S is a function of factors that affect its cost and benefit. This can be linearized as i * (4) S = η + λz + δm + v for i i i i i = 1,2,... N where the vector * M i Z i contains variables that affect the costs and benefits of schooling and is the expected net benefit from marriage in (1) and (2). Variables that cannot be observed are included in vi and the parameters to be estimated areη, λ andδ. As discussed earlier there are some factors unobserved to the econometrician that affect both schooling and marriage choices. In other words, ε i and v i are correlated Econometric Issues In the schooling and marriage models described above I assume that the unobservables in each case are independently and identically distributed as normal. The * parameter of interest is β. Ifε i and v i are not correlated and M i does not determine schooling (i.e., δ = 0) then a simple probit estimation of (2) and (3) would yield an estimate of β which would be the causal effect of schooling on marriage probabilities. However, that is not the case. I estimate equations (2), (3) and (4) using a two-stage method suggested by Lee and Maddala (1976) and Heckman (1978). To identify β, there must be at least one variable that is included in Z but not in X. Similarly, I can identify δ only if there is at least one variable in X that is not in Z. The variance-covariance matrix of the structural model defined by (2), (3) and (4) is defined by i i i i σ Ω = σ σ 12 σ 22 where σ 11 is the variance ofε i, σ 12 is the covariance of vi and ε andσ 22 is the variance i of v i. The two-stage method requires estimating the reduced form of (2) and (4) by probit and OLS and then plugging the predicted values of V and S back into (2) and (4) and 12 i i

24 solving them by probit and OLS, respectively. The variance-covariance matrix was derived by Maddala (1983) following the method used by Amemiya (1978) Data Data Description and Sample Selection To estimate the effect of schooling on marriage probabilities I use data from the 1979 National Longitudinal Survey of Youth (NLSY79). The NLSY79 is a survey of 12,686 respondents born between January 1, 1957 and December 31, It is an excellent choice for this study for the following reasons. First, it follows individuals during the period in their lives when they are primarily making marital, schooling and career decisions. The respondents were between the ages of 14 and 22 when they were first interviewed in They were interviewed annually until 1994 and biennially from then on. I use data until 2002 (data is available until 2004). Second, it has an over-sample of blacks; blacks constitute 25% of this sample. NLSY79 respondents are classified as Hispanic, non-hispanic black and non-hispanic non-black. I refer to the latter two categories as black and white, respectively. Third, the method of contacting those who missed an interview and bringing them back into the survey has reduced attrition. Those who are brought back into the survey are asked to report information since their last interview, thereby reducing information loss. I also use data from the Integrated Postsecondary Education Data System (IPEDS), the Higher Education General Information Survey (HEGIS) and the 1980, 1990 and 2000 decennial U.S. Census to construct some of the state and county level regressors as described later in this section. The IPEDS is a system of inter-related surveys which collect institution level information like tuition, enrollment, revenues and expenditures, faculty salaries from all post secondary institutions in the U.S. almost every year since The state and county of location for each of these institutions is also available. Similar information is available from the HEGIS for the years 1980, 1984 and The variance of the error term of the reduced form of (2) is normalized to one and all parameters can be estimated only up to its variance term. 13

25 The procedure I use to create the sample is detailed here and summarized in Table 2.1. Because Hispanics may differ in their behavior from non-hispanics of the same race I drop 2,002 Hispanic respondents from the sample. 4 The legal minimum age of marriage (without parental consent) is 18 years in all states except for Mississippi (where it is 21 years) and so I keep only those respondents who did not got married before they turned 18; only 515 respondents are dropped. By retaining only those interviewed at least until the age of 35 years the sample size drops to 6,878. Finally, I drop all those respondents who have missing information that could not be imputed or who have inconsistent or invalid information for other variables used in the estimation. The final sample size is 6,540. The proportion of women in this sample is 48.2% while it was around 50% in the original sample. In the original sample 30% of non-hispanics were blacks as compared to 38% of this sample Variables One of the dependent variable is the event of ever marrying (equation (2) and (3)) Persons are always at risk of marrying but the youngest respondents of the NLSY79 are observed until they are 38 years. In this study I proxy the variable ever married by ever married by age 35. I measure schooling attainment at the time of marriage. Measuring schooling attainment until respondents are last observed would be problematic, as it would include the schooling attained after marriage, perhaps as a direct consequence of the marriage. For those respondents who are not married by age 35, I measure it at age 35. Because I want to estimate the overall effect of schooling on marriage probabilities, which includes the effect of all factors that may have been influenced by a person s schooling (e.g., 4 While this race/ethnicity variable that classifies respondents as Hispanic, non-hispanic blacks and non- Hispanic non-blacks is the official variable used in NLSY79, alternative self-reported race and ethnicity information collected during the 1979 and 2002 surveys are available. Given that only 1.5% of the non- Hispanic non-blacks self-report themselves in these two interviews as Hispanics, I do not drop them from the sample. 5 In addition to blacks, the NLSY79 over-sampled Hispanics, military personnel and economically disadvantaged whites (poor whites). In 1990 this over-sample of poor whites was dropped from the survey. Because my sample consists of respondents who were interviewed until at least 35 years of age, the entire poor white over-sample is missing from my sample, making the proportion of whites much lower than in the original sample. 14

26 employment, occupation and earnings) I exclude these factors from the marriage equation. The instruments for schooling (i.e., variables included in Z but not in X and not correlated withε in equations (2) and (4) in section 2.3.1) are average in-state tuition at i public institutions (deflated by 2000 prices), the ratio of number of colleges to the number of persons between the ages of 18 and 24 years in the state, scores of Armed Forces Qualification Test (AFQT) and mother s highest grade completed and a dummy variable that takes on a value 1 if the respondent had access to newspapers, magazines or a library card at age 14. The first two variables are measured at the time of high school graduation; i.e., the date when the respondent completed grade 12 or received a GED or a high school diploma. If the person did not graduate from high school or this information is missing at the time of high school graduation these are measured at age 18 or at the earliest age between 14 and 25 when this information is available. In 1981 a battery of test was administered to most of the respondents interviewed that year called the Armed Services Vocational Aptitude Battery (ASVAB) and the AFQT score refers to the percentile composite score developed from parts of the battery of tests. The instruments for marriage (i.e., variables included in X but not in Z and not correlated with in equations (2) and (4) in section 2.3.1) are the sex ratio of the county v i of residence and the individual s body-mass index (BMI). The sex-ratio measures the women-men ratio in the population (in the age range of years) of the county of residence. The BMI can be interpreted as a crude proxy for physical appearance. Both are measured at the time of marriage for those getting married and by age 35 for those not married by that time. The other variables that I control for in the schooling and marriage equations are as follows. Family structure at age 14 is a four category variable; the four categories are if the respondent lived with both parents, lived with mother only, lived with father only and lived with some other guardian at age 14. Region of residence at age 14 is another four category variable where the four categories are whether the individual resided in the south, northeast, north central and west regions of the U.S. at age 14. Next I include a binary variable which indicates whether the respondent resided in an urban area at age 15 i i i i

27 14. I also include number of siblings, number of older siblings of the respondent as reported in Religious affiliation as reported in 1979 is another four category variable that I use none, Baptist, other Protestant denominations and Roman Catholic. Almost every religion encourages marriage but only some allow or encourage divorce. Thus a person s religious affiliation (including none) is likely to play an important role in determining marital behavior or at least attitudes towards marriage. Finally religiosity as reported in 1979 measures the frequency of attending religious services. The three categories are attends weekly, attends monthly and does not attend. This further indicates the degree of influence that religious beliefs are likely to have on a person s behavior. Religious meetings may serve as marriage markets because people of similar religious views meet there Sample Statistics I note here a few striking patterns in marital behavior and schooling attainment. These are shown in Tables 2.2 and 2.3. First, as noted extensively in previous studies, I find that black marriage rates are lower than white marriage rates. Fraction of whites married by age 35 is 0.84 as compared to 0.59 for blacks (see Table 2.2). The racial difference in marriage rates is slightly higher for women than for men (0.26 for women and 0.24 for men). Second, I find that while marriage rates are lower among higher schooling categories for white men and women, the opposite is true of black men. Third, schooling patterns in this sample shows that blacks have lower schooling attainment than whites. While 23.4% of white have completed 16 or more years of schooling only 10.3% of blacks have done so (see Table 2.3). Percentage of blacks dropping out of high school is also higher than that of whites 19.9% of blacks vis-à-vis 11.2% of whites. This implies that there is scope for increasing marriage rates of blacks by increasing their schooling attainment, if such causality is established. Blacks and whites have known to differ widely in indicators of economic and social advantages that are likely to affect schooling and marriageability. Table 2.4 shows the difference in means for blacks and whites with respect to such variables. Blacks come 16

28 from larger families, are less likely to live in households with both parents and their mother s schooling is slightly lower than whites (by about one grade). All these point to the higher financial constraints of blacks. Also, they have a lower AFQT score on an average than whites (around 54 for whites as compared to 23 for blacks). Moreover, about 95% of whites in comparison to only 82% of blacks had access to a library card or received magazines or newspapers regularly when they were Although 85% to 92% of both races report some religious affiliation, I find a striking difference in the pattern of their religious affiliation. The predominant religious group among whites is Roman Catholics and other Protestant denominations while among blacks it is Baptist, followed by other Protestant denominations. Another striking difference is in their religiosity; blacks attend religious service more frequently than whites do. Finally, I find that in this sample blacks were raised predominantly in the south and in urban areas. About 60% of blacks were raised in the south as opposed to only 30% of whites and around 80% of blacks were raised in urban areas as compared to 75% of whites. Given these strong racial differences in determinants of marriage other than schooling it would be interesting to see how schooling compares to these variables in explaining racial differences in marriage probabilities. 2.5 Results Estimated Coefficients of the Marriage Model Estimated marginal effects and z-statistics for the marriage equation (based on joint estimation of schooling and marriage) are reported in Table 2.5. I find that the schooling of all but white women has a positive effect on their probabilities of being married by age 35. If the schooling of black men is raised from the mean by one year then their probability of marrying by age 35 increases by 5.9%. The corresponding numbers for white men, black women and white women are 0.9%, 2.2% and -1.2%, respectively. These are statistically significant for white women and black men at the 5% 6 I do not consider AFQT as a proxy for intelligence or innate ability but as a measure of skills that have been acquired and so determined partly by environmental factors including family background (Currie and Thomas 1999). 17

29 level and for black women and white men at the 15% level. 7 The results for black and white men are consistent with the discussions in section 2.2. Those discussions had also revealed that women s schooling has opposing effects on their marriage probabilities and so the final result would depend on the relative strengths of these opposing effects. It is interesting to note that schooling has opposite effects on the marriage probabilities of white and black women. The estimated schooling parameters in the marriage equations reveal that if schooling is treated as exogenous, the estimated coefficients are lower than they are when it is treated as endogenous to marriage (see Table 2.8). If the schooling of black men were to be increased from the mean by one year then their probability of marrying by age 35 would rise by 2%. The corresponding number for all other groups is negative; these are -2%, -1% and -2% for white men, black women and white women, respectively. These are statistically significant at the 5% level for all but black women; for them it is significant only at the 15% level. I also find that the return to marriage has a negative effect on schooling (see Table 2.7). It follows that once its effect was eliminated in the two-stage estimation the effect of schooling on marriage probabilities increased. I re-estimated the two-stage model for the same sample using age 25 as the age cut-off for ever married to see if schooling has similar effects on early marriage behavior as it does on overall marital behavior (see Table 2.9). The schooling here is the schooling acquired by first marriage if the person was married by age 25 and by age 25 if the person was not married by age 25. I find that marginal effects are negative for all four demographic groups but these are not statistically significant at the 10% level for any of them. If the primary effect of schooling on marriage probabilities operates via the effect of schooling on earnings then it would make sense that any positive effect would be evident only at a later age when the careers of individuals would have been established (Bergstrom and Schoeni 1996). Hardly any of the regressors have any statistically 7 I also estimate this model after including the per capita family income variable as one of the regressors for schooling. The results are quite similar. The marginal effects of schooling on marriage probabilities (by age 35) are slightly higher in magnitude for black men and women and slightly lower in magnitude for white women. These estimates are available upon request from the author. 18

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